Reduce to lowest terms: $- \dfrac{5}{7} \div \dfrac{1}{7} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{1}{7}$ is $ \dfrac{7}{1}$ Therefore: $ - \dfrac{5}{7} \div \dfrac{1}{7} = - \dfrac{5}{7} \times \dfrac{7}{1} $ $ \phantom{- \dfrac{5}{7} \times \dfrac{7}{1}} = \dfrac{-5 \times 7}{7 \times 1} $ $ \phantom{- \dfrac{5}{7} \times \dfrac{7}{1}} = \dfrac{-35}{7} $ The numerator and denominator have a common divisor of $7$, so we can simplify: $ \dfrac{-35}{7} = \dfrac{-35 \div 7}{7 \div 7} = -5 $